Scientists who carried out scans of the King's spine found it had a "well balanced curve" that could have been concealed under clothes or custom-made armour.
Unlike the hunchback depictions seen on stage and screen, his head and neck would have been straight, not tilted, and there is no evidence he had a limp.
The findings are backed by accounts written during Richard III's lifetime which describe him as "comely enough" and "handsome".
A skeleton found under a Leicester car park in 2012 was confirmed as the king's last year after DNA testing.
In the new study, experts carried out a 3D reconstruction of the spine which showed 65 to 85 degrees of scoliosis, or bending, to the right. It was also twisted into a spiral shape. But despite having one shoulder slightly higher than the other and a short trunk compared with his arms and legs, the defects would not have handicapped the him too much.
Dr Phil Stone, chairman of the Richard III Society, said: "Examination of Richard III's remains shows he had a scoliosis, thus confirming the Shakespearean description of a 'bunch-backed toad' is a complete fabrication."
For the study, published in The Lancet medical journal, CT scans of the bones and a 3D printer were used to create a plastic model of the spine.
Dr Jo Appleby, from Leicester University, who led the research, said: "Although the scoliosis looks dramatic, it probably did not cause a major physical deformity.
"A curve of 65-85 would not have prevented Richard from being an active individual."